Natural Forms

Forms in my backyard

Evolving condensation forms seen from the Verandah | Source

Everywhere we look

Every aspect of our lives is affected by it. All the practical actions we take, our mental processes, the way we think: all are founded on Natural Forms. What are these forms, these shapes? We see them daily in everything we see, everything we do, everywhere we look. The are a necessary part of our lives, our daily work, ourselves as human beings.

What I would like to do here today is to mention a few of the Forms, to describe them and briefly illustrate how they are incorporated in what we see in nature and in what we build and use, both privately and culturally.

Types of Natural Forms

As I sit here thinking, I realize I may have bitten off a little more than I can easily masticate. That's OK though; this is a first foray into the topic and other episodes may follow. I will list forms as they occur to me.

1) The Straight line

2) The Curve

3) The Polygon

4) The Dendritic Construction

5) The Meander

6) Fractals as Natural Forms

Straight lines, Curves and Fractal Forms | Source

The Straight Line

What is most interesting is that in nature the straight lines we see are the product of an inanimate, physical Necessity, the example being the formation of crystals, where the facet edges are perfect or near-perfect constructions. Perfect to a matter of atoms. We, or I at least, must bow to this exactitude. It's replication in the factory is by simple imitation of the inanimate physical process. With as much respect as I have for artists, living or dead, the replication of the Truly Straight Line is not in their Provence.

The Curve

The Calculus is a mode of mathematical calculation. It deals with curving lines and the area which may be measured beneath them. If this is an oversimplification, please cool your Larry Lightbulb brains simply realize I am speaking to my Fellows, the Great Unwashed. Yes. I have studied Calculus both In High School and at the University but I will never claim a real understanding if I might have a real appreciation for its Beauty. Calculus is a little like Go. The simplest of games, learnable in minutes, Profound in its machinations. So too, Calculus, simple in its presentation, often workmanlike in its use, still profound in implications.

Isaac Newton may have developed it first; Leibniz in Germany may have first described it. Since English is my first language, I tend to think of Newton first. The argument has gone on for several centuries. I think a good way to think of it is that Integral Calculus, with its beautiful sloping large SSes, standing for Summation, I suppose, may be attributed to Sir Isaac. The Differential branch of Calculus we may give to Leibniz.

My point has to do with differentials. I cursed them, I loathed them as I thought of Leibniz scribbling his eternal calculations and me wishing I had an easy visual memory device to finally understand these things. After a lot of reading and more than a little scribbling, I think I finally understand. And now I will tell you. Please don't howl too loudly. The single point at which a straight line intersects a curve tangentially is that curve's Differential. A Curve may be seen as a geometrical surface on which the differential changes point by point. I think.

Curves may be more 'regular', as we see in the Conic sections (look it up!) or drawn with artistic freedom. We see them everywhere And will touch on the topic again when we briefly discuss Fractals below.

Fractal shapes in nature

Curves

A beautiful series of Curves and, I think, a series by Fibonacci as well. | Source

The Polygon

A polygon might be seen as an iteration of the straight line. Physical forces as in quartz crystal formation or hard-wired construction protocols seen in insect nest building result in similar shapes. The main idea here is that these regular constructions each use the space they must and that in their construction no excess form is used to encompass the maximum space. I think Buckminster Fuller was an Insect or a Force of Nature at heart.

One of the most interesting and challenging aspects of personal faith is that in thinking about Natural Forms in our surrounding lives, they may be seen in two ways. God may deign the existence of a crystal in a repeatable form. A beautiful form, a beautiful idea. At the same time, though, the precise physical laws which act irregardless of our presence to appreciate the elegant result are seen in action around us, by me as Scientist and Secular Physician. Again, I see all life as being within a circumscribed lacuna in a Venn Diagram, The Universe being the Provence of God and the lacuna itself, the 'Real World', also a part of this universe and the action of God within it being possible but not always necessary. Confused? My faith is an old one but satisfying . Christ asked that his followers follow his edict: 'Be Ye as little children.' What does this mean, though? In grade school, we walked in two lines following Sister, a boy's line and a girl's line. We kept quiet and obeyed the Rules. Is this what Christ meant? I don't think so. What did He mean, 'be thee as a child?' Imagine a small child. It always asks questions. It doubts everything, privately if not out loud. It misbehaves in its frustration. It refuses to accept the Reason, the Explanation, the Plan. I think This is what Christ meant: not the sterile, immobile belief of a little caricature but a living, doubting and developing faith of a child.

Random but firmly subscribed and ordered by Physical Laws | Source

Another Natural Form: A Living Dendritic Construction

Turn it on its side: it looks like a Southern California Oak | Source

The Dendritic Construction

The nerve cell, from the single receiving end (axon) to the further-dispersing end (dendrite) is the functional unit of the nervous system. It relays a pulse along its' tube in one direction only. This involves the electrochemical exchange of sodium going into the tube as potassium leaves. The pulse thus engendered moves along. Speaking Of natural forms, this same regulated transfer of information is seen at every football game. 'The Wave' is an exact analogy of the transfer of a neural impulse, writ large. At the far end of the cell the impulse is sent via the dendrites to any large number of other axons which further relay the impulse along. The Wave has a precise, predictable speed. In similar wyse the speed of a neural transmission is what it is, no faster or slower. Someone who seems to react faster to changing environments, a professional athlete or a seasoned mercenary in a firefight, has no faster nerve transmission. This suggests the faster reaction time is the result of a practiced simplification of the number of outcomes and the quick willingness to follow the decided path. You shoot the ball or the enemy without further thought. How is this machination of impulses going along an increasingly complex dendritic net a thought or whatever? Who knows? Secular Science has its articles of faith, too.

In nature we see dendritic elaborations in many places. Trees expanding into the air as they grow in a pattern predictable by species but each tree individually different look little different in general form from a human lung viewed on its side.

The neural sheath surrounding the nerve cell is made of a series of living cells, the Oligodendrocytes, which themselves wrap around the nerve tube and provide insulation. (Doesn't this get in the way of sodium and potassium transfer across the cell membrane? No.) In MS, the Oligodendrocyttes are declared as being Foreign and are attacked, denuding the nerve sheathe and markedly slowing/disrupting impulse transmission. Ergo, I don't dance very well. This is hyper-simplification but is true enough for us all to basically understand the dendritic spray as an example of a Natural Form.

A CA Oak, Rightside Up | Source

The Meander

The Meander may be my favorite natural form It is most commonly seen by us Hoi Polloi in photographs or scenes in film or our own minds of the gently flowing, wandering, Meandering of a river or stream. It's path looks random and uncontrolled and so Peaceful! It is not random and is fully controlled and predictable by the secular physical laws that we see everywhere in the natural forms. Also, in the process of its development, it may not be gentle.

I am not a mathematician but if I were, I would spend more time studying Fractals. My reading on this topic promised explanation but left me confused. In my experience, when I read something and don't understand it, it likely means that the guy who wrote the text didn't know what he was talking about and freely dispensed his ignorance into the Ether. I see this a lot in medical literature. Fractals, so absorbing and startlingly beautiful, must be understandable with study.

the point is that the Meander appears the same in any scale viewed, Amazonian to nearly microscopic, as you will see in Fractals. The flow pattern seen in the Mississippi is that we can see close up along the bank of an Arizona arroyo.

This pattern is one of the most satisfying Natural Forms. We see the overlap of Frontal and Parietal cranial plates in a view of the Father of Waters from low orbit. The peisoelectric forces which define near-final skull bone edge placement are similarly recapitulated in the settlement of River loams. The suggestion is that the forces involved must be either the same or closely similar. They must be of related Type. The fractal nature of each instance, the deposition of dirt and of bone, the exact similarity of result when viewed on a macro- or microscopic scale, is obvious.

The meander in pictures

The skull with meandering plate edges. | Source

A meander from low orbit. | Source

Another Natural form

A cyclone approaching Florida: The Coriolus effect as seen from Space. | Source

Final words

I may come back to this topic. I love it, the beauty of its concepts, the many available pictures. The action of God in nature is never clearly shown but consideration of the possibility is attractive to me.Faith can't be made too easy!

These pictures are not mine. I appreciate their easy availability and wish I could always correctly attribute their sources.